The fraction of DA white dwarfs with kilo-gauss magnetic fields, ABSTRACT

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1 A&A 462, (2007) DOI: / : c ESO 2007 Astronomy & Astrophysics The fraction of DA white dwarfs with kilo-gauss magnetic fields, S. Jordan 1, R. Aznar Cuadrado 2, R. Napiwotzki 3,H.M.Schmid 4, and S. K. Solanki 2 1 Astronomisches Rechen-Institut, Zentrum für Astronomie der Universität Heidelberg, Mönchhofstr , Heidelberg, Germany jordan@ari.uni-heidelberg.de 2 Max-Planck-Institut für Sonnensystemforschung, Max-Planck-Str. 2, Katlenburg-Lindau, Germany [aznar;solanki]@linmpi.mpg.de 3 Centre for Astrophysics Research, University of Hertfordshire, Hatfield AL10 9AB, UK rn@star.herts.ac.uk 4 Institut für Astronomie, ETH Zürich, 8092 Zürich, Switzerland schmid@astro.phys.ethz.ch Received 2 August 2006 / Accepted 12 October 2006 ABSTRACT Context. Weak magnetic fields have been searched for on only a small number of white dwarfs. Current estimates find that about 10% of all white dwarfs have fields in excess of 1 MG; according to previous studies this number increases up to about 25% in the kg regime. Aims. Our aim is to improve on these statistics by a new sample of ten white dwarfs in order to determine the ratio of magnetic to field-free white dwarfs. Methods. Mean longitudinal magnetic fields strengths were determined by means of high-precision circular polarimetry of Hβ and Hγ with the FORS1 spectrograph of the VLT Kueyen 8 m telescope. Results. In one of our objects (LTT 7987), we detected a statistically significant (97% confidence level) longitudinal magnetic field varying between ( 1±0.5) kg and (+1±0.5) kg. This would be the weakest magnetic field ever found in a white dwarf, but systematic errors cannot completely be ruled out at this level of accuracy. We also observed the sdo star EC but could not detect a magnetic field. Conclusions. VLT observations with uncertainties typically of 1000 G or less suggest that 15 20% of WDs have kg fields. Together with previous investigations, the fraction of kg magnetic fields in white dwarfs amounts to about 11 15%, which is close to the current estimations for highly magnetic white dwarfs (>1MG). Key words. stars: white dwarfs stars: magnetic fields 1. Introduction The question of how many white dwarfs are magnetic has been actively debated in the recent years. In about 170 of the 5500 white dwarfs listed in the online version of the Villanova White Dwarf Catalog ( magnetic fields between 2 kg and 1 GG have been measured, corresponding to a fraction of about 3% (McCook & Sion 1999; Wickramasinghe & Ferrario 2000; Vanlandingham et al. 2005). However, the spectra of only a few of the known white dwarfs have been examined for the presence of a magnetic field in enough detail. Liebert et al. (2003) and Schmidt et al. (2003) estimate that the true fraction of white dwarfs with magnetic fields in excess of 2 MG is expected to be at least 10% and maybeashighas20%. Until recently, magnetic fields below 30 kg could not be detected, with the exception of the very bright white dwarf 40 Eri B (V = 8.5), in which Fabrika et al. (2003) found a magnetic field Based on observations made with ESO Telescopes at the La Silla or Paranal Observatories under programme ID 073.D Figures A.1 and A.2 are only available in electronic form at of 4 kg. However, by using the ESO VLT, we could push the detection limit down to about 1 kg in our first investigation of 12 DA white dwarfs with 11 < V < 14 (Aznar Cuadrado et al. 2004). In 3 objects of this sample, we detected magnetic fields between 2 kg and 7 kg on a 5σ confidence level. Therefore, we concluded that the fraction of white dwarfts with kg magnetic fields is about 25%. For one of our cases, LP (WD ), Valyavin et al. (2006) confirm the presence of a kg magnetic field by measuring circular polarisation at Hα using the 6 m of the Special Astrophysical Observatory. On the other hand, none of the other 5 bright white dwarfs of their sample showed any significant signature of a magnetic field. They detected a magnetic field of up to 10 kg in the hot subdwarf (spectral type sdo) Feige 34, confirming the detection of magnetic fields in both types of white dwarf progenitors, hot subdwarfs (O Toole et al. 2005) and central stars of planetary nebulae (Jordan et al. 2005). With this new investigation, we increase the sample of white dwarfs that is checked for kg magnetic fields by means of circular polarisation by eleven objects (one turned out to be a highmetallicity sdo, Stys et al. 2000). This should allow us to provide a much better estimate of the incidence of low magnetic fields in white dwarfs. Article published by EDP Sciences and available at or

2 1098 S. Jordan et al.: The fraction of DA white dwarfs with kilo-gauss magnetic fields Table 1. Details of the VLT observations. Target Alias α δ V HJD t exp n T sp (mag) ( ) (s) WD EC sdo WD EC DA WD G DA WD CD DA WD Lan DA WD GD DA WD LTT DA WD RE DA WD LTT DA WD G DA WD RE DA All tables have been organised in exactly the same way as in Aznar Cuadrado et al. (2004, Paper I); the figures show the same spectral regions as in Paper I but have been plotted in a more compact way. 2. Observations and data reduction The spectropolarimetric data of our new sample of ten bright normal DA white dwarfs plus one high-metallicity sdo star were obtained in service mode between May 5 and August 4, 2004, with the FORS1 spectrograph at the 8 m UT2 ( Kueyen ) of the VLT. The setup was exactly the same as described in Paper I. The spectra and circular polarimetric data covered the wavelength region between 3600 Å and 6000 Å with a spectral resolution of 4.5 Å. A higher spectral resolution would not provide a higher sensitivity since the accuracy is basically limited by the signalto-noise ratio allone. The exposures were split into a sequence of exposures to avoid saturation; after every second observation the retarder plate was rotated from α = 45 to α =+45 and back in order to suppress spurious signals in the degree of circular polarisation (calculated from the ratio of the Stokes parameters V and I). All stars were observed in two or three different nights in order to detect the presence of possible variations in V/I due to the rotation of the stars. As in the case of the sample of Paper I, all objects in our new sample of DA white dwarfs have been previously observed in the course of the SPY survey (Napiwotzki et al. 2003), a radial velocity search for close binary systems composed of two white dwarfs. We checked all candidates for spectral peculiarities and magnetic fields strong enough to be detected in intensity spectra taken with the high-resolution Echelle spectrograph UVES at the Kueyen (UT2) of the VLT. None of our programme stars showed any sign of Zeeman splitting in the SPY SURVEY, i.e., indicating that any possible magnetic field must be below a level of about 20 kg. The data reduction and calculation of the observed circular polarisation is described in detail in Paper I. Special care was taken to avoid errors from changes in the sky transparency, atmospheric scintillation, and various instrumental effects. The wavelength calibration was made for each observing date separately, and no spurious signals were detected during the calibration process. Details of our eleven sample stars and of our observations are listed in Table 1. The provided α and δ coordinates refer to epoch 2000 as measured in the course of the SPY project (see Koester et al. 2001). Spectral types, T sp, and measured V magnitudes were taken from the catalogue of McCook & Sion (1999). EC was classified as an DAO white dwarf by Kilkenny et al. (1997). 3. Determination of magnetic fields As discussed in Paper I, the theoretical V/I profile for a given mean longitudinal magnetic field B z (expressed in Gauss) below about 10 kg is given by the weak-field approximation (e.g. Angel & Landstreet 1970; Landi degl Innocenti & Landi degl Innocenti 1973) without any loss in accuracy: V I = g effc z λ 2 1 I I λ B z, (1) where g eff is the effective Landé factor (=1 for all hydrogen lines of any series, Casini & Landi degl Innocenti 1994), λ is the wavelength expressed in Å, and the constant C z = e/(4πm e c 2 ) ( G 1 Å 1 ). We again performed a χ 2 -minimisation procedure to find out which mean longitudinal magnetic field strength fits the observed data best in wavelength intervals of ±20 Å around Hβ and Hγ. Since the error of the magnetic field determination increases for the higher series number, we based our investigation onlyonthesetwobalmerlines.

3 S. Jordan et al.: The fraction of DA white dwarfs with kilo-gauss magnetic fields 1099 Table 2. Magnetic fields derived from the Hγ and Hβ lines for our sample of white dwarfs. Target Date σ(v) B(G) B(G) B(σ) B(G) at 1σ (10 3 I c ) Hγ Hβ Hγ, β Hγ, β Hγ Hβ WD /05/ ± ± ± /05/ ± ± ± average ± ± ± WD /05/ ± ± ± /05/ ± ± ± average ± ± ± WD /05/ ± ± ± /05/ ± ± ± average ± ± ± WD /05/ ± ± ± /05/ ± ± ± /05/ ± ± ± average ± ± ± WD /05/ ± ± ± /05/ ± ± ± average ± ± ± WD /05/ ± ± ± /05/ ± ± ± average ± ± ± WD /05/ ± ± ± /05/ ± ± ± average ± ± ± WD /05/ ± ± ± /06/ ± ± ± /06/ ± ± ± average ± ± ± WD /05/ ± ± ± /06/ ± ± ± average ± ± ± WD /06/ ± ± ± /07/ ± ± ± /08/ ± ± ± average ± ± ± WD /05/ ± ± ± /06/ ± ± ± average ± ± ± The resulting best-fit values for the magnetic field strengths from the individual lines and their statistical 1σ errors are listed in Table 2 for each observation. B(σ) provides the magnetic field in units of the σ level. Detections exceeding the 2σ levels are given in bold. σ(v) is the standard deviation of the observed (V/I)-spectrum obtained in the region Å. Lower limits on the detectability of the magnetic field from the line polarisation peaks, calculated at the 1σ level of the noise, are given in the last two columns. Multiple observations that were averaged prior to analysis are labeled average.wealso provid the weighted means B z = (B z,γ w γ + B z,β w β )/(w γ + w β ) where w i = 1/σ 2 i (i = γ, β). The probable error is given by σ = ( w i ) 1/2. Moreover, we expressed the resulting mean magnetic field in multiples of the 1σ error in order to judge the significance of the magnetic field determination. For a comparison we note that for each of the three stars with significant magnetic fields from the Aznar Cuadrado et al. (2004) sample, at least one observation exceeded the 5σ level. In Table 2 we also calculated lower limits on the detectability of the magnetic fields from the line polarisation peaks, which guide the eye when judging the confidence of the fits from plots of the circular polarisation (Fig. 1 and online Fig. A.1). Note, however, that a significant contribution to the fit originates not only from the narrow peaks but also from the full 40 Å interval around the Balmer lines. Note, however, that in the three magnetic cases of our first study, the S-wave circular polarisation signature reaches the 2σ level of the noise. For each object we also added up all measurements according to formula 3 in Paper I. The results for these added observations were labeled as average. Our fitting procedure was validated with extensive numerical simulations using a large sample of 1000 artificial noisy polarisation spectra (Aznar Cuadrado et al. 2004). It was found that at our noise level σ(v) (also listed in Table 2) of some 10 3 I c (I c being the continuum intensity), kg fields can reliably be detected. 4. Results EC (WD ) is a high-gravity pre-white dwarf of spectral type sdo, which we disregard in our statistics on white dwarfs, but whose measurement is interesting on its own. The nature of this star with T eff = K and log g = 5.8 has been revealed by Stys et al. (2000). As can be seen from Table 2, Fig. 1, and Fig. A.1 (online only), none of the measurements of the circular polarisations reached the same level of confidence as the three magnetic objects found in the first sample (Paper I). The highest level of confidence was achieved by LTT 7987 (WD ) where

4 1100 S. Jordan et al.: The fraction of DA white dwarfs with kilo-gauss magnetic fields Fig. 1. Circular polarisation spectra V/I (thin black lines) around Hβ (4861 Å, right), Hγ (4340 Å, middle), and close to the Balmer threshold (left) for those observations, where the 2σ level is exceeded. The thick lines (red in the online version) represent the circular polarisation predicted by the low-field approximation (Eq. (1)), using the values for the longitudinal magnetic field from the best fit to the Hβ and Hγ regions. For comparison we also plotted the result for BPM 0352 with B = 6321 G (lowest panel), which was analysed by Aznar Cuadrado et al. (2004). The plots of all other observations are shown in Fig. A.1 of the online version. a2.4 and2.0σ level was reached for the two respective observations. The corresponding mean longitudinal field strengths were 1093 ± 453 G and 970 ± 485 G. Single observations of CD (WD ) resulted in 1116 ± 406 G and LTT 8189 (WD ) in 1297±512G, which corresponds to 2.8σ and 2.5σ, respectively. In Paper I we disregarded the case of LHS 1270, for which a magnetic field of 654 ± 320 G was found. Since their sample consisted of 22 single observations, statistically one would expect this 2σ observation even if all the stars have no magnetic field. Our new sample consists of 23 single observations of white dwarfs and two observations of a metal-rich sdo. With the same argument we would statistically expect only one observation to exceed the 2σ level. Therefore, one can assume that between none and three of the observations may actually be a real observation. With two observations exceeding 2σ, LTT 7987 (WD ) would be the most convincing for a positive detection. The probability that two independent and uncorrelated observations of a single star have that level of confidence can be estimated in the following way: the likelihood that an observation exceeds 2σ is 4.6%; therefore, the chance that at least one observation of the white dwarfs exceeds 2σ is ( ) = 66.1%. Then the probability that the same star has a second observation exceeding 2σ is = 3.0%. Therefore, from a purely statistical point of view, we must regard this detection as significant (with 97% confidence). However, we have to take into account that the measured magnetic field strengths would be only about 1 kg, which is 2 to 6 times smaller than the positive detections from the sample of Paper I. At this level we cannot fully exclude systematic errors from the limitation of our low-field approximation (assuming a single magnetic strength rather than a distribution) or from instrumental polarisation. However, Bagnulo et al. (2006) have shown that none of their observed non-magnetic A stars observed with the same instrument showed circular polarization hinting at magnetic fields larger than 400 G. This would mean that the systematic errors are well below 1 kg. On the other hand, none of the polarisation peaks of LTT 7987 in Fig. 1 exceeds the noise level, differently from the three detections BPM 03523, LP , and L in Aznar Cuadrado et al. (2004). Therefore, a χ-by-eye analysis would not confirm our detection but, as we pointed out in Paper I, this would be very misleading. Both measurements of the sdo star EC are below the 2σ level. This is interesting in itself and confirms the finding by O Toole et al. (2005) that there is no correlation between the metallicity and the presence of a magnetic field with kg strength. Therefore, we conclude that although the measured magnetic field in LTT 7987 is statistically significant, further observations are needed to establish their reality. In order to find out whether white dwarfs with and without kg magnetic fields differ in mass or age, we computed masses and cooling ages from the fundamental atmospheric parameters temperature and gravity. The values of T eff and log g were derived from a model atmosphere analysis of the high signal-tonoise spectra (see Fig. 2 in the online material). The observed line profiles are fitted with theoretical spectra from a large grid of NLTE spectra calculated with the NLTE code developed by Werner (1986). The four coolest white dwarfs of our sample (WD , WD , and WD ) were analysed with a grid of LTE model spectra computed by D. Koester for the analysis of DA white dwarfs (see e.g. Finley et al. 1997), which is more reliable below K, where convection and collision-induced absorption by hydrogen quasi-molecules play arole. Table 3 lists the results of the model atmosphere analyses. From these we determined spectroscopic distances, as well as masses and cooling ages computed from a comparison of parameters derived from the fit with the grid of white dwarf cooling sequences by Benvenuto & Althaus (1999), for an envelope hydrogen mass of 10 4 M WD. A temperature-gravity diagram with the positions of white dwarfs analysed in Paper I and in the current paper is shown in Fig. 2. In Table 3 we also provid data collected from the literature (atmospheric parameters, rotational velocities, and trigonometic parallaxes) when available. 5. Conclusion While we detected magnetic fields in 3 out of the 12 programme stars in our first investigation, we found at most (if at all) one object in our new sample of 10 DA white dwarfs. Putting both samples together, we arrive at a fraction of 14 18% of kg magnetism in white dwarfs; the lower value is obtained assuming that LTT 7987 is not magnetic. However, if confirmed, LTT 7987 would have the lowest magnetic field (1 kg) ever detected in a white dwarf. Recently, Valyavin et al. (2006) also performed a search for circular polarisation in white dwarfs. They confirmed our

5 S. Jordan et al.: The fraction of DA white dwarfs with kilo-gauss magnetic fields 1101 Table 3. Fitted parameters of the white dwarfs and supplementary data from literature. literature WD T eff log g M d(spec) t cool T eff log g v sin i d(trig) (kk) (M ) (pc) (Myr) (kk) (km s 1 ) (pc) WD <6 7 WD ± 1 2 WD < ± WD WD < ± 3 5 WD < ± 1 2 WD <14 4 WD < ± 2 2 WD ± 3 2 WD References: 1 Bragaglia et al. (1995); 2 Perryman et al. (1997); 3 Koester et al. (1998); 4 Karl et al. (2005); 5 van Altena et al. (1995); 6 Finley et al. (1997); 7 Berger et al. (2005). ones (Liebert 1988) does not seem to exist for magnetic white dwarfs with kg fields. This would be consistent with the idea that the high-magnetic-field white dwarfs have a higher-thanaverage mass because they have more massive progenitors. Therefore, it is probable that the white dwarfs with kg magnetic fields stem from a low-mass progeny on the main sequence (e.g. F stars) as speculated by Wickramasinghe & Ferrario (2005). Acknowledgements. We acknowledge the use of LTE model spectra computed by D. Koester, Kiel. We thank the staff of the ESO VLT for carrying out the service observations. We thank U. Bastian, Heidelberg, for suggestions concerning the correct application of statistics. G. Mathys and S. Bagnulo, both at ESO, have contributed to our project with valuable discussions. Fig. 2. Temperature-gravity diagram with the positions of white dwarfs analysed in Paper I and in the current paper. Theoretical cooling sequences from Benvenuto & Althaus (1999) are plotted for various white dwarf masses. White dwarfs with and without detected magnetic fields are indicated by different symbols. The double-lined binary WD from Paper I is not shown in this plot. detection (Aznar Cuadrado et al. 2004) of a varying longitudinal magnetic field in LP (WD ): they measured field strengths between 7.9 ± 2.6kGto0.1 ± 2.7 kg, compared to our values of 4.0 ± 0.7kG to 2.1 ± 0.4 kg. However, they did not discover any significant magnetic field in their five other programme stars. If we combine their results with our s, the fraction of kg magnetic fields in DA white dwarfs amounts to 15% (4/( )) or 11% (3/( )), if we disregard the detection in LTT However, it is problematic to merge both samples, because the signal-to-noise ratio of our VLT measurements is much higher than the observations with the 6 m telescope of the Special Astrophysical Observatory. Since our uncertainties are on the average 2 3 times smaller (partly also due to the fact that Valyavin et al only used Hα), we must put a higher statistical weight on our sample with a fraction of 11% to 15% of magnetic to field-free (i.e. below detection limit) white dwarfs. While one of the white dwarfs with a magnetic field (L ) had an exceptionally high mass (0.95 M ), all objects with kg magnetic fields have usual white dwarf masses in the range 0.5 to 0.6 M. Therefore, a trend towards higher masses in magnetic white dwarfs compared to non-magnetic References Angel, J. R. P., & Landstreet, J. D. 1970, ApJ, 160, L147 Aznar Cuadrado, R., Jordan, S., Napiwotzki, R., et al. 2004, A&A, 423, 1081 Bagnulo, S., Landstreet, J. D., Mason, E., et al. 2006, A&A, 450, 777 Benvenuto, O. G., & Althaus, L. G. 1999, MNRAS, 303, 30 Berger, L., Koester, D., Napiwotzki, R., Reid, I. N., & Zuckermann, B. 2005, A&A, 565, 571 Bragaglia, A., Renzini, A., & Bergeron, P. 1995, ApJ, 443, 735 Casini, R., & Landi degl Innocenti, E. 1994, A&A, 291, 668 Fabrika, S. N., Valyavin, G. G., & Burlakova, T. E. 2003, Astron. Lett., 29, 737 Finley, D. S., Koester, D., & Basri, G. 1997, ApJ, 488, 375 Jordan, S., Werner, K., & O Toole 2005, A&A, 432, 273 Karl, C. A., Napiwotzki, R., Heber, U., et al. 2005, A&A, 434, 637 Kilkenny, D., O Donoghue, D., Koen, C., Stobie, R. S., & Chen, A. 1997, MNRAS, 287, 867 Koester, D., Dreizler, S., Weidemann, V., & Allard, N. F. 1998, A&A, 338, 612 Koester, D., Napiwotzki, R., Christlieb, N., et al. 2001, A&A, 378, 556 Landi degl Innocenti, E., & Landi degl Innocenti, M. 1973, Solar Phys., 29, 287 Landstreet, J. D. 1982, ApJ, 258, 639 Liebert, J. 1988, PASP, 100, 1302 Liebert, J., Bergeron, P., & Holberg, J. B. 2003, AJ, 125, 348 McCook, G. P., & Sion, E. M. 1999, ApJS, 121, 1 Napiwotzki, R., Christlieb, N., Drechsel, H., et al. 2003, ESO-Messenger, 112, 25 O Toole, S. J., Jordan, S., Friedrich, S., & Heber, U. 2005, A&A, 437, 227 Perryman, M. A. C., Lindegren, L., Kovalevsky, J., et al. 1997, A&A, 323, L49 Schmidt, G. D., Harris, H. C., Liebert, J., et al. 2003, ApJ, 595, 1101 Stys, D., Slevinsky, R., Sion, E. M., & Saffer, R PASP, 112, 354 Valyavin, G., Bagnulo, S., Fabrika, S., et al. 2006, ApJ, in press [arxiv:astro-ph/ ] vanaltena,w.f.,lee,j.t.,&hoffleit, E. D. 1995, The general catalogue of trigonometric parallaxes, 4th Ed. (New Haven: Yale University Observatory) Vanlandingham, K. M., Schmidt, G. D., Eisenstein, D. J., et al. 2005, AJ, 130, 734 Werner, K. 1986, A&A, 161, 177 Wickramasinghe, D. T., & Ferrario, L. 2000, PASP, 112, 873 Wickramasinghe, D. T., & Ferrario, L. 2005, MNRAS, 356, 1576

6 S. Jordan et al.: The fraction of DA white dwarfs with kilo-gauss magnetic fields, Online Material p 1 Online Material

7 S. Jordan et al.: The fraction of DA white dwarfs with kilo-gauss magnetic fields, Online Material p 2 Appendix A: Fig. A.1. Circular polarisation spectra V/I (thin black lines) for different observing dates in the regions around Hβ (4861 Å, right), Hγ (4340 Å, middle), and close to the Balmer threshold (left) for those measurements, where no significant magnetic field could be detected. The red thick lines represent the circular polarisation predicted by the low-field approximation (Eq. (1)) using the values for the longitudinal magnetic field from the best fit to the Hβ and Hγ regions.

8 S. Jordan et al.: The fraction of DA white dwarfs with kilo-gauss magnetic fields, Online Material p 3 Fig. 2. Model atmosphere fits (solid line) for the mean of all measured spectra (dashed line) of the white dwarfs. The results for T eff and log g are given in Table 3.